English

Length-Preserving Directions and Some Diophantine Equations

Number Theory 2021-06-24 v1 Spectral Theory

Abstract

We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail, and also discuss the extension to the three-dimensional case.

Keywords

Cite

@article{arxiv.2106.12019,
  title  = {Length-Preserving Directions and Some Diophantine Equations},
  author = {Juan Tolosa},
  journal= {arXiv preprint arXiv:2106.12019},
  year   = {2021}
}

Comments

5 figures

R2 v1 2026-06-24T03:29:06.168Z